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In this work we establish a Stokes-type integral equality for scalarlyessentially integrable forms on an orientable smooth manifold with values inthe locally convex linear space $\langle B(G),\sigma(B(G),\mathcal{N})\rangle$,where $G$ is a complex Banach space and $\mathcal{N}$ is a suitable linearsubspace of the norm dual of $B(G)$. This result widely extends theNewton-Leibnitz-type equality stated in one of our previous articles. To obtainour equality we generalize the main result of that article, and employ theStokes theorem for smooth locally convex vector valued forms established in aprodromic paper. Two facts are remarkable. Firstly the forms integratedinvolved in the equality are functions of a possibly unbounded scalar typespectral operator in $G$. Secondly these forms need not be smooth nor evencontinuously differentiable.

Stokes-type Integral Equalities for Scalarly Essentially Integrable  Locally Convex Vector Valued Forms which are Functions of an Unbounded  Spectral Operator